Hydrogels having exceptionally good bio-compatibility have been developed. These gels are based on hyaluronan, which is hyaluronic acid and its salts, and/or hylan and its salts. They are also based on hyaluronan or hylan cross-linked with DVS (FIGS. 1 and 2, see also U.S. Pat. Nos. 4,605,691 and 6,521,223), and/or cross-linked mixtures of hyaluronan with other polymers or low molecular weight substances (U.S. Pat. No. 4,582,865). Hylan A is a water soluble hyaluronan preparation chemically modified by covalent cross-linking with small amounts of an aldehyde, typically formaldehyde, while hylan B is hylan A further cross-linked by DVS (see U.S. Pat. No. 4,713,448). Gel slurries prepared from hyaluronan, chemically modified hyaluronan and hylan have also been described (U.S. Pat. No. 5,143,724). Such hydrogels may be used for drug delivery (U.S. Pat. No. 4,636,524) and other purposes in the medical field. However, these gels and gel slurries are non-elastic, non-cohesive, and non-adhesive.